My mac mini keeps restarting on its own. Have reinstalled OS twice. Diagnostics finds no issues. Anybody offer any suggestions? Apple support cannot figure it out.

What year model Mac Mini?

see > https://support.apple.com/en-us/HT201894

Could be a bad power supply, but it sounds more like a bad/loose wall outlet or bad power cord.

1. Reset the SMC as per the desktop instructions at > https://support.apple.com/en-us/HT201295
2. Go to Apple > System Preferences > Energy Saver > uncheck "Startup automatically after a power failure" then if the Mac Mini looses power it will stay off and not restart automatically.
3. Check the power cord connection on the back of the Mac Mini and at the wall outlet to make sure that they are snug and not loose.
4. Try moving the Mac Mini to another wall outlet.
5. Try another power cord.

If none of that leads you to the problem, then it's time to make a service appointment at you local Apple Authorized Service Provider.